A method for reducing the sensitivity of optimal nonlinear systems to parameter uncertainty
Method for reducing sensitivity of optimal nonlinear systems to parameter uncertainty
Elliott, J. R.↗
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Failure Analysis of the Method of Adjoint Systems to Determine Optimal Trajectories
Failure analysis of adjoint systems method for determining optimal trajectories
FAILURE MODE↗
Airfoil optimization by the one-shot method
An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (Governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Language multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.
Kuruvila, G.↗
Airfoil Design and Optimization by the One-Shot Method
An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Lagrange multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.
Kuruvila, G.↗
Robust eigenstructure assignment by a projection method: Application using multiple optimization criteria
New ideas which lead to feedback control laws for large flexible structures which are insensitive to model uncertainty are presented. A pole placement method is presented which leads to near-unitary closed loop eigenvectors, and a new method is introduced to design the control while simultaneously considering three competing measures of optimality. Robustness versus Integral algorithms are applicable to at least moderately high-dimensioned systems. In the present discussion, controls for two coupled flexible bodies are considered. A 6x24 gain matrix is designed to control a 12 modes system using 6 actuators. Researchers also developed control laws for the R2P2 simulator at Martin Marietta; in this case 3 actuators are used to control a 12th order system. Simulation studies indicate that researchers indeed achieved robust designs without significant difficulties associated with spillover into the uncontrolled modes. Here, several key ideas and numerical results are given. In the references, details of the formulation, discussions of salient features, and connection to the availiable literature are given.
Junkins, J. L.↗
Viscous aerodynamic design using the adjoint variable approach
The use of classical optimal control methods, in particular variational methods, to solve the airfoil optimization problem, by deriving a set of adjoint (costate) equations and boundary conditions has already been done for inviscid (potential and Euler flows) and two dimensional, steady state, incompressible flow governed by the Navier-Stokes equations. The interior and boundary terms of the volume integral have been derived (in this work) for the steady Navier-Stokes equations in three dimensions for a viscous, compressible heat conducting fluid. This can be used to derive the adjoint equations and numerical boundary conditions for general classes of problems and hence paves the way for a solution to the aerodynamic optimization problem for compressible viscous flows. The next steps to the realization of that goal are projected as below. The usual square integral pressure functional as an objective function is being replaced by a more realistic drag functional subject to a lift constraint. The feasibility of attempting the more difficult time dependent problem is being investigated. It remains to get the full system of adjoint equations and boundary conditions with the new functional. The state and adjoint equations must be discretized and coded. An appropriate optimization program must be used (steepest descents seems inadequate) and various known airfoil shapes should be recovered in test cases of the computer program.
DeRise, George↗
Detection of fatigue cracks by nondestructive testing methods
The effectiveness was assessed of various NDT methods to detect small tight cracks by randomly introducing fatigue cracks into aluminum sheets. The study included optimizing NDT methods calibrating NDT equipment with fatigue cracked standards, and evaluating a number of cracked specimens by the optimized NDT methods. The evaluations were conducted by highly trained personnel, provided with detailed procedures, in order to minimize the effects of human variability. These personnel performed the NDT on the test specimens without knowledge of the flaw locations and reported on the flaws detected. The performance of these tests was measured by comparing the flaws detected against the flaws present. The principal NDT methods utilized were radiographic, ultrasonic, penetrant, and eddy current. Holographic interferometry, acoustic emission monitoring, and replication methods were also applied on a reduced number of specimens. Generally, the best performance was shown by eddy current, ultrasonic, penetrant and holographic tests. Etching provided no measurable improvement, while proof loading improved flaw detectability. Data are shown that quantify the performances of the NDT methods applied.
Anderson, R. T.↗
GASP Advancements With Symbolic Computations, Optimization, and Decoupled Numerical Methods
NASA is exploring advancements in hybrid-electric propulsion concepts for aircraft design. A new analysis capability has been deployed at NASA’s Ames Research Center using a new mathematical modeling framework in Python that leverages symbolic representation of mathematical expressions, optimization-based problem formulations, and standalone numerical methods. This capability, called Gascon, has been verified against NASA’s General Aviation Synthesis Program (GASP) results for several vehicles that exercise the analysis capability for a variety of aircraft classes and engine models, including both turbofans and turboprops. We believe this capability will set the stage for more rapid development of novel aircraft models with more flexible design assessments using optimization, and more traceable analysis for reproducibility. Additionally, a novel Pareto optimization-based design space exploration that shows the trade between range flown and fuel burn by manipulating the thrust split during cruise for a true parallel hybrid aircraft was developed by leveraging the unique features of Gascon.
aircraft design↗
The suitability of selected multidisciplinary design and optimization techniques to conceptual aerospace vehicle design
Four methods for preliminary aerospace vehicle design are reviewed. The first three methods (classical optimization, system decomposition, and system sensitivity analysis (SSA)) employ numerical optimization techniques and numerical gradients to feed back changes in the design variables. The optimum solution is determined by stepping through a series of designs toward a final solution. Of these three, SSA is argued to be the most applicable to a large-scale highly coupled vehicle design where an accurate minimum of an objective function is required. With SSA, several tasks can be performed in parallel. The techniques of classical optimization and decomposition can be included in SSA, resulting in a very powerful design method. The Taguchi method is more of a 'smart' parametric design method that analyzes variable trends and interactions over designer specified ranges with a minimum of experimental analysis runs. Its advantages are its relative ease of use, ability to handle discrete variables, and ability to characterize the entire design space with a minimum of analysis runs.
Olds, John R.↗
Parameter optimization of a nutation damper via the second method of Liapunov
Parameter optimization of linear time invariant nutation damper by second Liapunov method
Sen, A. K.↗
Neural Network and Regression Methods Demonstrated in the Design Optimization of a Subsonic Aircraft
The neural network and regression methods of NASA Glenn Research Center s COMETBOARDS design optimization testbed were used to generate approximate analysis and design models for a subsonic aircraft operating at Mach 0.85 cruise speed. The analytical model is defined by nine design variables: wing aspect ratio, engine thrust, wing area, sweep angle, chord-thickness ratio, turbine temperature, pressure ratio, bypass ratio, fan pressure; and eight response parameters: weight, landing velocity, takeoff and landing field lengths, approach thrust, overall efficiency, and compressor pressure and temperature. The variables were adjusted to optimally balance the engines to the airframe. The solution strategy included a sensitivity model and the soft analysis model. Researchers generated the sensitivity model by training the approximators to predict an optimum design. The trained neural network predicted all response variables, within 5-percent error. This was reduced to 1 percent by the regression method. The soft analysis model was developed to replace aircraft analysis as the reanalyzer in design optimization. Soft models have been generated for a neural network method, a regression method, and a hybrid method obtained by combining the approximators. The performance of the models is graphed for aircraft weight versus thrust as well as for wing area and turbine temperature. The regression method followed the analytical solution with little error. The neural network exhibited 5-percent maximum error over all parameters. Performance of the hybrid method was intermediate in comparison to the individual approximators. Error in the response variable is smaller than that shown in the figure because of a distortion scale factor. The overall performance of the approximators was considered to be satisfactory because aircraft analysis with NASA Langley Research Center s FLOPS (Flight Optimization System) code is a synthesis of diverse disciplines: weight estimation, aerodynamic analysis, engine cycle analysis, propulsion data interpolation, mission performance, airfield length for landing and takeoff, noise footprint, and others.
Hopkins, Dale A.↗
Efficient Parameterization of Density Functional Tight-Binding for 5 f -Elements: A Th–O Case Study
Density functional tight binding (DFTB) models for f-element species are challenging to parametrize owing to the large number of adjustable parameters. The explicit optimization of the terms entering the semiempirical DFTB Hamiltonian related to f orbitals is crucial to generating a reliable parametrization for f-block elements, because they play import roles in bonding interactions. However, since the number of parameters grows quadratically with the number of orbitals, the computational cost for parameter optimization is much more expensive for the f-elements than for the main group elements. In this work we present a set of efficient approaches for mitigating the hurdle imposed by the large size of the parameter space. A novel group-by-orbital correction functions for two-center bond integrals was developed. With this approach the number of parameters is reduced, and it grows linearly with the number of elements, maintaining the accuracy and the number of parameters, in the case of f elements, by more than 40%. The parameter optimization step was accelerated by means of the mini-batch BFGS method. This method allows parameter optimizations with much larger training sets than other single batch methods. A stochastic optimizer was employed that helped overcome shallow local minima in the objective function. The proposed algorithm was used to parametrize the DFTB Hamiltonian for the Th–O system, which was subsequently applied to the study of ThO 2 nanoparticles. The training set consisted of 6322 unique structures, which is barely feasible with conventional optimization methods. The optimized parameter set, LANL-ThO, displays good agreement with DFT-calculated properties such as energies, forces, and structures for both clusters and bulk ThO 2 . Benefiting from the fewer number of parameters and lower computational costs for objective function evaluations, this new approach shows its potential applications in DFTB parametrization for elements with high angular momentum, which present a challenge to conventional methods.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems
NASA's space data-communications infrastructure, the Space Network and the Ground Network, provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft via orbiting relay satellites and ground stations. An implementation of the methods and algorithms disclosed herein will be a system that produces globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary search, a class of probabilistic strategies for searching large solution spaces, constitutes the essential technology in this disclosure. Also disclosed are methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithm itself. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally, with applicability to a very broad class of combinatorial optimization problems.
Rash, James L.↗
An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems
NASA's space data-communications infrastructure-the Space Network and the Ground Network-provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft. The Space Network operates several orbiting geostationary platforms (the Tracking and Data Relay Satellite System (TDRSS)), each with its own servicedelivery antennas onboard. The Ground Network operates service-delivery antennas at ground stations located around the world. Together, these networks enable data transfer between user spacecraft and their mission control centers on Earth. Scheduling data-communications events for spacecraft that use the NASA communications infrastructure-the relay satellites and the ground stations-can be accomplished today with software having an operational heritage dating from the 1980s or earlier. An implementation of the scheduling methods and algorithms disclosed and formally specified herein will produce globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary algorithms, a class of probabilistic strategies for searching large solution spaces, is the essential technology invoked and exploited in this disclosure. Also disclosed are secondary methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithms themselves. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure within the expected range of future users and space- or ground-based service-delivery assets. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally. The generalized methods and algorithms are applicable to a very broad class of combinatorial-optimization problems that encompasses, among many others, the problem of generating optimal space-data communications schedules.
ground stations↗
On the removal of ill conditioning effects in the computation of optimal controls
Dual type method solving discrete optimal control problems with linear plants, convex cost and constraint taking into account dynamic structure
Polak, E.↗
Method and Apparatus for Providing In-Flight Pilot Interface for Trajectory Optimization
Systems and methods of an in-cockpit flight trajectory modification system for an aircraft are provided. A receiver is capable of receiving flight-related hazard information. A traffic aware planner (TAP) module is operably connected to the receiver to receive the flight-related hazard information. A user interface device is operably connected to the TAP module on board the aircraft to provide trajectory information associated with the aircraft and to receive user input corresponding to a request for a revised trajectory. A TAP application is capable of calculating one or more revised trajectories for the aircraft based at least on active trajectory information of the aircraft and the flight-related hazard information. The user interface device may be configured to display information related to the one or more revised trajectories, including a graphic display of the active trajectory and at least one revised trajectory in a visualization panel of the user interface device.
Burke, Kelly Ann↗
Properties of ionization breakdown of air at microwave frequencies and optimization of component dimensions for maximum microwave power
Method provides optimization of dimensions in vented RF components for predictable performance at critical pressures, eliminates leakage from hermetically sealed types, and utilizes coaxial RF multicouplers.
Rainwater, L. L.↗
An approach to optimization of low-power Stirling cryocoolers
A method for optimizing the design (shape of the displacer) of low power Stirling cryocoolers relative to the power required to operate the systems is described. A variational calculation which includes static conduction, shuttle and radiation losses, as well as regenerator inefficiency, was completed for coolers operating in the 300 K to 10 K range. While the calculations apply to tapered displacer machines, comparison of the results with stepped displacer cryocoolers indicates reasonable agreement.
Sullivan, D. B.↗